(éditeur) [...] The other precision of PPP is its use of carrier-phase measurements rather than just pseudoranges. Carrier-phase measurements have a precision on the order of two magnitudes (a factor of 100) better than that of pseudoranges. But there is a catch to the use of carrier-phase measurements: they are ambiguous by an integer multiple of one cycle. Processing algorithms must resolve the value of this ambiguity and ideally fix it at its correct integer value. Unfortunately, it is difficult to do this instantaneously, and often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy, say better than 10 centimeters. Researchers are actively working on reducing the convergence time, and this month'column, we look at how using measurements from three satellite frequencies rather than just two can help.

(auteur) We study sequences of optimal walks of a growing length in weighted digraphs, or equivalently, sequences of entries of max-algebraic matrix powers with growing exponents. It is known that these sequences are eventually periodic when the digraphs are strongly connected. The transient of such periodicity depends, in general, both on the size of digraph and on the magnitude of the weights. In this paper, we show that some bounds on the indices of periodicity of (unweighted) digraphs, such as the bounds of Wielandt, Dulmage–Mendelsohn, Schwarz, Kim and Gregory–Kirkland–Pullman, apply to the weights of optimal walks when one of their ends is a critical node.

(Auteur) Integer ambiguity resolution at a single receiver can be achieved if the fractional-cycle biases are separated from the ambiguity estimates in precise point positioning (PPP). Despite the improved positioning accuracy by such integer resolution, the convergence to an ambiguity-fixed solution normally requires a few tens of minutes. Even worse, these convergences can repeatedly occur on the occasion of loss of tracking locks for many satellites if an open sky-view is not constantly available, consequently totally destroying the practicability of real-time PPP. In this study, in case of such re-convergences, we develop a method in which ionospheric delays are precisely predicted to significantly accelerate the integer ambiguity resolution. The effectiveness of this method consists in two aspects: first, wide-lane ambiguities can be rapidly resolved using the ionosphere-corrected wide-lane measurements, instead of the noisy Melbourne–Wübbena combination measurements; second, narrow-lane ambiguity resolution can be accelerated under the tight constraints derived from the ionosphere-corrected unambiguous wide-lane measurements. In the test at 90 static stations suffering from simulated total loss of tracking locks, 93.3 and 95.0% of re-convergences to wide-lane and narrow-lane ambiguity resolutions can be achieved within five epochs of 1-Hz measurements, respectively, even though the time latency for the predicted ionospheric delays is up to 180 s. In the test at a mobile van moving in a GPS-adverse environment where satellite number significantly decreases and cycle slips frequently occur, only when the predicted ionospheric delays are applied can the rate of ambiguity-fixed epochs be dramatically improved from 7.7 to 93.6% of all epochs. Therefore, this method can potentially relieve the unrealistic requirement of a continuous open sky-view by most PPP applications and improve the practicability of real-time PPP.